By performing microscopic charge transport simulations for a set of crystalline dicyanovinyl-substituted oligothiophenes, we find that the internal acceptor-donor-acceptor molecular architecture combined with thermal fluctuations of dihedral angles results in large variations of local electric fields, substantial energetic disorder, and pronounced Poole-Frenkel behavior, which is unexpected for crystalline compounds. We show that the presence of static molecular dipoles causes large energetic disorder, which is mostly reduced not by compensation of dipole moments in a unit cell but by molecular polarizabilities. In addition, the presence of a well-defined pi-stacking direction with strong electronic couplings and short intermolecular distances turns out to be disadvantageous for efficient charge transport since it inhibits other transport directions and is prone to charge trapping.